On the T(q)-conditions of small cancellation theory
type: Item
instance of: scholarly article
title: On the T(q)-conditions of small cancellation theory
zbMATH Open document ID: 0584.20026
DOI: 10.1007/BF02774082
author: Stephen J. Pride
author: Alfred D. Vella
author: Patricia M. Hill
published in: Israel Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: Small cancellation conditions for presentations of groups were introduced and studied by \textit{R. Lyndon} [Math. Ann. 166, 208-228 (1966; Zbl 0138.257)] and others. In the paper under review a graphical method is given which can be used to determine whether or not a group presentation satisfies the small cancellation condition T(q). This method is used to deterimine all 2- and 3-generator presentations satisfying T(4). Similar arguments can also be applied to n-generator presentations where \(n\geq 4\) but the amount of labor involved in carrying out the requisite calculations by hand is more and more prohibitive. \{Reviewer's remark: A related paper by \textit{D. J. Collins} and the reviewer [Math. Ann. 261, 155-183 (1982; Zbl 0477.20019)] is not among the references.\}
Mathematics Subject Classification ID: 20F06
zbMATH DE Number: 3935307
zbMATH Keywords: presentations
zbMATH Keywords: graphical method
zbMATH Keywords: small cancellation condition
reviewed by: J. Huebschmann
MaRDI profile type: Publication
cites work: Q5572939
cites work: Cohomology theory of aspherical groups and of small cancellation groups
cites work: Q3877854
cites work: Q4145882
cites work: Q3955568
cites work: Q3341041
full work available at URL: https://doi.org/10.1007/bf02774082
OpenAlex ID: W1981099917
description: scientific article; zbMATH DE number 3935307